{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "from statsmodels.tsa import stattools\n",
    "%matplotlib inline\n",
    "from matplotlib import pyplot as plt\n",
    "from pandas.plotting import autocorrelation_plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#we always start by setting the current directory and then working relative to it\n",
    "os.chdir('D:/Practical Time Series')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "djia_df = pd.read_excel('datasets/DJIA_Jan2016_Dec2016.xlsx')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Date</th>\n",
       "      <th>Open</th>\n",
       "      <th>High</th>\n",
       "      <th>Low</th>\n",
       "      <th>Close</th>\n",
       "      <th>Adj Close</th>\n",
       "      <th>Volume</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2016-01-04</td>\n",
       "      <td>17405.480469</td>\n",
       "      <td>17405.480469</td>\n",
       "      <td>16957.630859</td>\n",
       "      <td>17148.939453</td>\n",
       "      <td>17148.939453</td>\n",
       "      <td>148060000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2016-01-05</td>\n",
       "      <td>17147.500000</td>\n",
       "      <td>17195.839844</td>\n",
       "      <td>17038.609375</td>\n",
       "      <td>17158.660156</td>\n",
       "      <td>17158.660156</td>\n",
       "      <td>105750000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2016-01-06</td>\n",
       "      <td>17154.830078</td>\n",
       "      <td>17154.830078</td>\n",
       "      <td>16817.619141</td>\n",
       "      <td>16906.509766</td>\n",
       "      <td>16906.509766</td>\n",
       "      <td>120250000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2016-01-07</td>\n",
       "      <td>16888.359375</td>\n",
       "      <td>16888.359375</td>\n",
       "      <td>16463.630859</td>\n",
       "      <td>16514.099609</td>\n",
       "      <td>16514.099609</td>\n",
       "      <td>176240000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2016-01-08</td>\n",
       "      <td>16519.169922</td>\n",
       "      <td>16651.890625</td>\n",
       "      <td>16314.570313</td>\n",
       "      <td>16346.450195</td>\n",
       "      <td>16346.450195</td>\n",
       "      <td>141850000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>2016-01-11</td>\n",
       "      <td>16358.709961</td>\n",
       "      <td>16461.849609</td>\n",
       "      <td>16232.030273</td>\n",
       "      <td>16398.570313</td>\n",
       "      <td>16398.570313</td>\n",
       "      <td>127790000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>2016-01-12</td>\n",
       "      <td>16419.109375</td>\n",
       "      <td>16591.349609</td>\n",
       "      <td>16322.070313</td>\n",
       "      <td>16516.220703</td>\n",
       "      <td>16516.220703</td>\n",
       "      <td>117480000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>2016-01-13</td>\n",
       "      <td>16526.630859</td>\n",
       "      <td>16593.509766</td>\n",
       "      <td>16123.200195</td>\n",
       "      <td>16151.410156</td>\n",
       "      <td>16151.410156</td>\n",
       "      <td>153530000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>2016-01-14</td>\n",
       "      <td>16159.009766</td>\n",
       "      <td>16482.050781</td>\n",
       "      <td>16075.120117</td>\n",
       "      <td>16379.049805</td>\n",
       "      <td>16379.049805</td>\n",
       "      <td>158830000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>2016-01-15</td>\n",
       "      <td>16354.330078</td>\n",
       "      <td>16354.330078</td>\n",
       "      <td>15842.110352</td>\n",
       "      <td>15988.080078</td>\n",
       "      <td>15988.080078</td>\n",
       "      <td>239210000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        Date          Open          High           Low         Close  \\\n",
       "0 2016-01-04  17405.480469  17405.480469  16957.630859  17148.939453   \n",
       "1 2016-01-05  17147.500000  17195.839844  17038.609375  17158.660156   \n",
       "2 2016-01-06  17154.830078  17154.830078  16817.619141  16906.509766   \n",
       "3 2016-01-07  16888.359375  16888.359375  16463.630859  16514.099609   \n",
       "4 2016-01-08  16519.169922  16651.890625  16314.570313  16346.450195   \n",
       "5 2016-01-11  16358.709961  16461.849609  16232.030273  16398.570313   \n",
       "6 2016-01-12  16419.109375  16591.349609  16322.070313  16516.220703   \n",
       "7 2016-01-13  16526.630859  16593.509766  16123.200195  16151.410156   \n",
       "8 2016-01-14  16159.009766  16482.050781  16075.120117  16379.049805   \n",
       "9 2016-01-15  16354.330078  16354.330078  15842.110352  15988.080078   \n",
       "\n",
       "      Adj Close     Volume  \n",
       "0  17148.939453  148060000  \n",
       "1  17158.660156  105750000  \n",
       "2  16906.509766  120250000  \n",
       "3  16514.099609  176240000  \n",
       "4  16346.450195  141850000  \n",
       "5  16398.570313  127790000  \n",
       "6  16516.220703  117480000  \n",
       "7  16151.410156  153530000  \n",
       "8  16379.049805  158830000  \n",
       "9  15988.080078  239210000  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "djia_df.head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#Let us parse the Date column and use as row index for the DataFrame and drop it as a column\n",
    "djia_df['Date'] = pd.to_datetime(djia_df['Date'], '%Y-%m-%d')\n",
    "djia_df.index = djia_df['Date']\n",
    "djia_df.drop('Date', axis=1, inplace=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
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       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Open</th>\n",
       "      <th>High</th>\n",
       "      <th>Low</th>\n",
       "      <th>Close</th>\n",
       "      <th>Adj Close</th>\n",
       "      <th>Volume</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2016-01-04</th>\n",
       "      <td>17405.480469</td>\n",
       "      <td>17405.480469</td>\n",
       "      <td>16957.630859</td>\n",
       "      <td>17148.939453</td>\n",
       "      <td>17148.939453</td>\n",
       "      <td>148060000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-05</th>\n",
       "      <td>17147.500000</td>\n",
       "      <td>17195.839844</td>\n",
       "      <td>17038.609375</td>\n",
       "      <td>17158.660156</td>\n",
       "      <td>17158.660156</td>\n",
       "      <td>105750000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-06</th>\n",
       "      <td>17154.830078</td>\n",
       "      <td>17154.830078</td>\n",
       "      <td>16817.619141</td>\n",
       "      <td>16906.509766</td>\n",
       "      <td>16906.509766</td>\n",
       "      <td>120250000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-07</th>\n",
       "      <td>16888.359375</td>\n",
       "      <td>16888.359375</td>\n",
       "      <td>16463.630859</td>\n",
       "      <td>16514.099609</td>\n",
       "      <td>16514.099609</td>\n",
       "      <td>176240000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-08</th>\n",
       "      <td>16519.169922</td>\n",
       "      <td>16651.890625</td>\n",
       "      <td>16314.570313</td>\n",
       "      <td>16346.450195</td>\n",
       "      <td>16346.450195</td>\n",
       "      <td>141850000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-11</th>\n",
       "      <td>16358.709961</td>\n",
       "      <td>16461.849609</td>\n",
       "      <td>16232.030273</td>\n",
       "      <td>16398.570313</td>\n",
       "      <td>16398.570313</td>\n",
       "      <td>127790000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-12</th>\n",
       "      <td>16419.109375</td>\n",
       "      <td>16591.349609</td>\n",
       "      <td>16322.070313</td>\n",
       "      <td>16516.220703</td>\n",
       "      <td>16516.220703</td>\n",
       "      <td>117480000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-13</th>\n",
       "      <td>16526.630859</td>\n",
       "      <td>16593.509766</td>\n",
       "      <td>16123.200195</td>\n",
       "      <td>16151.410156</td>\n",
       "      <td>16151.410156</td>\n",
       "      <td>153530000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-14</th>\n",
       "      <td>16159.009766</td>\n",
       "      <td>16482.050781</td>\n",
       "      <td>16075.120117</td>\n",
       "      <td>16379.049805</td>\n",
       "      <td>16379.049805</td>\n",
       "      <td>158830000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-01-15</th>\n",
       "      <td>16354.330078</td>\n",
       "      <td>16354.330078</td>\n",
       "      <td>15842.110352</td>\n",
       "      <td>15988.080078</td>\n",
       "      <td>15988.080078</td>\n",
       "      <td>239210000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    Open          High           Low         Close  \\\n",
       "Date                                                                 \n",
       "2016-01-04  17405.480469  17405.480469  16957.630859  17148.939453   \n",
       "2016-01-05  17147.500000  17195.839844  17038.609375  17158.660156   \n",
       "2016-01-06  17154.830078  17154.830078  16817.619141  16906.509766   \n",
       "2016-01-07  16888.359375  16888.359375  16463.630859  16514.099609   \n",
       "2016-01-08  16519.169922  16651.890625  16314.570313  16346.450195   \n",
       "2016-01-11  16358.709961  16461.849609  16232.030273  16398.570313   \n",
       "2016-01-12  16419.109375  16591.349609  16322.070313  16516.220703   \n",
       "2016-01-13  16526.630859  16593.509766  16123.200195  16151.410156   \n",
       "2016-01-14  16159.009766  16482.050781  16075.120117  16379.049805   \n",
       "2016-01-15  16354.330078  16354.330078  15842.110352  15988.080078   \n",
       "\n",
       "               Adj Close     Volume  \n",
       "Date                                 \n",
       "2016-01-04  17148.939453  148060000  \n",
       "2016-01-05  17158.660156  105750000  \n",
       "2016-01-06  16906.509766  120250000  \n",
       "2016-01-07  16514.099609  176240000  \n",
       "2016-01-08  16346.450195  141850000  \n",
       "2016-01-11  16398.570313  127790000  \n",
       "2016-01-12  16516.220703  117480000  \n",
       "2016-01-13  16151.410156  153530000  \n",
       "2016-01-14  16379.049805  158830000  \n",
       "2016-01-15  15988.080078  239210000  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Let us see first few rows of the modified DataFrame\n",
    "djia_df.head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#We would be using the 'Close' values of the DJIA to illustrate Differencing\n",
    "first_order_diff = djia_df['Close'].diff(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x21520bbc438>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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PmZFAn0j+G7DeM5NxPWVcel/ge7ftYWJfAE2AV7FukqOALbN5MwULvvooLbU+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\nHxAQEFCjCAQfEBAQUKP4X+0YLxURgaDtAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x21520ab4ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Let us plot the original time series and first-differences\n",
    "fig, ax = plt.subplots(2, sharex=True)\n",
    "fig.set_size_inches(5.5, 5.5)\n",
    "djia_df['Close'].plot(ax=ax[0], color='b')\n",
    "ax[0].set_title('Close values of DJIA during Jan 2016-Dec 2016')\n",
    "first_order_diff.plot(ax=ax[1], color='r')\n",
    "ax[1].set_title('First-order differences of DJIA during Jan 2016-Dec 2016')\n",
    "#plt.savefig('plots/ch2/B07887_02_06.png', format='png', dpi=300)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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cdCAT9TadM4dM1DtWOh+gqvtXFSmjDEykiMg8Ve2VbDkSTSbqbTpn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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x21522092c18>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Let us plot the ACFs of original time series and first-differences\n",
    "fig, ax = plt.subplots(2, sharex=True)\n",
    "fig.set_size_inches(5.5, 5.5)\n",
    "autocorrelation_plot(djia_df['Close'], color='b', ax=ax[0])\n",
    "ax[0].set_title('ACF of DJIA Close values')\n",
    "autocorrelation_plot(first_order_diff.iloc[1:], color='r', ax=ax[1])\n",
    "ax[1].set_title('ACF of first differences of DJIA Close values')\n",
    "plt.tight_layout(pad=0.4, w_pad=0.5, h_pad=2.0)\n",
    "plt.savefig('plots/ch2/B07887_02_07.png', format='png', dpi=300)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'\\nNow we will perform the Ljung-Box test on the ACFs\\nof the original time series and the first-differences.\\nFor running the test we will limit upto 20 lags\\n'"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"\n",
    "Now we will perform the Ljung-Box test on the ACFs\n",
    "of the original time series and the first-differences.\n",
    "For running the test we will limit upto 20 lags\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "Let us obtain the confidence intervls, Ljung-Box Q-statistics and p-values\n",
    "for the original DJIA Close values\n",
    "\"\"\"\n",
    "acf_djia, confint_djia, qstat_djia, pvalues_djia = stattools.acf(djia_df['Close'],\n",
    "                                                                 unbiased=True,\n",
    "                                                                 nlags=20,\n",
    "                                                                 qstat=True,\n",
    "                                                                 alpha=0.05)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Null hypothesis is rejected at lag = 0 for p-val = 1.06937677537e-55\n",
      "Null hypothesis is rejected at lag = 1 for p-val = 9.99432646963e-107\n",
      "Null hypothesis is rejected at lag = 2 for p-val = 3.51431863547e-156\n",
      "Null hypothesis is rejected at lag = 3 for p-val = 8.30678314236e-204\n",
      "Null hypothesis is rejected at lag = 4 for p-val = 1.33852326465e-249\n",
      "Null hypothesis is rejected at lag = 5 for p-val = 1.19209433653e-293\n",
      "Null hypothesis is rejected at lag = 6 for p-val = 0.0\n",
      "Null hypothesis is rejected at lag = 7 for p-val = 0.0\n",
      "Null hypothesis is rejected at lag = 8 for p-val = 0.0\n",
      "Null hypothesis is rejected at lag = 9 for p-val = 0.0\n",
      "Null hypothesis is rejected at lag = 10 for p-val = 0.0\n",
      "Null hypothesis is rejected at lag = 11 for p-val = 0.0\n",
      "Null hypothesis is rejected at lag = 12 for p-val = 0.0\n",
      "Null hypothesis is rejected at lag = 13 for p-val = 0.0\n",
      "Null hypothesis is rejected at lag = 14 for p-val = 0.0\n",
      "Null hypothesis is rejected at lag = 15 for p-val = 0.0\n",
      "Null hypothesis is rejected at lag = 16 for p-val = 0.0\n",
      "Null hypothesis is rejected at lag = 17 for p-val = 0.0\n",
      "Null hypothesis is rejected at lag = 18 for p-val = 0.0\n",
      "Null hypothesis is rejected at lag = 19 for p-val = 0.0\n"
     ]
    }
   ],
   "source": [
    "\"\"\"Let us check if at confidence level 95% (alpha=0.05)\n",
    "if the null hypothesis is rejected at any of the lags\n",
    "\"\"\"\n",
    "alpha = 0.05\n",
    "for l, p_val in enumerate(pvalues_djia):\n",
    "    if p_val > alpha:\n",
    "        print('Null hypothesis is accepted at lag = {} for p-val = {}'.format(l, p_val))\n",
    "    else:\n",
    "        print('Null hypothesis is rejected at lag = {} for p-val = {}'.format(l, p_val))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'\\nThe above results show statistically significant ACF in the original DJIA Close values\\n'"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"\n",
    "The above results show statistically significant ACF in the original DJIA Close values\n",
    "\"\"\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "Let us obtain the confidence intervls, Ljung-Box Q-statistics and p-values\n",
    "for the differenced DJIA Close values\n",
    "\"\"\"\n",
    "acf_first_diff, confint_first_diff,\\\n",
    "qstat_first_diff, pvalues_first_diff = stattools.acf(first_order_diff.iloc[1:],\n",
    "                                                     unbiased=True,\n",
    "                                                     nlags=20,\n",
    "                                                     qstat=True,\n",
    "                                                     alpha=0.05)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Null hypothesis is accepted at lag = 0 for p-val = 0.17569800898\n",
      "Null hypothesis is accepted at lag = 1 for p-val = 0.353830085301\n",
      "Null hypothesis is accepted at lag = 2 for p-val = 0.553139564033\n",
      "Null hypothesis is accepted at lag = 3 for p-val = 0.698512780756\n",
      "Null hypothesis is accepted at lag = 4 for p-val = 0.789158012067\n",
      "Null hypothesis is accepted at lag = 5 for p-val = 0.877290328278\n",
      "Null hypothesis is accepted at lag = 6 for p-val = 0.901277483583\n",
      "Null hypothesis is accepted at lag = 7 for p-val = 0.942982316238\n",
      "Null hypothesis is accepted at lag = 8 for p-val = 0.948591655652\n",
      "Null hypothesis is accepted at lag = 9 for p-val = 0.93779779437\n",
      "Null hypothesis is accepted at lag = 10 for p-val = 0.893761260743\n",
      "Null hypothesis is accepted at lag = 11 for p-val = 0.915219093022\n",
      "Null hypothesis is accepted at lag = 12 for p-val = 0.926324524389\n",
      "Null hypothesis is accepted at lag = 13 for p-val = 0.9350725554\n",
      "Null hypothesis is accepted at lag = 14 for p-val = 0.940439468541\n",
      "Null hypothesis is accepted at lag = 15 for p-val = 0.959577855985\n",
      "Null hypothesis is accepted at lag = 16 for p-val = 0.944327330315\n",
      "Null hypothesis is accepted at lag = 17 for p-val = 0.816772704234\n",
      "Null hypothesis is accepted at lag = 18 for p-val = 0.700742545631\n",
      "Null hypothesis is accepted at lag = 19 for p-val = 0.57145506907\n"
     ]
    }
   ],
   "source": [
    "\"\"\"Let us check if at confidence level of 95% (alpha = 0.05)\n",
    "if the null hypothesis is rejected at any of the lags\n",
    "\"\"\"\n",
    "alpha = 0.05\n",
    "for l, p_val in enumerate(pvalues_first_diff):\n",
    "    if p_val > alpha:\n",
    "        print('Null hypothesis is accepted at lag = {} for p-val = {}'.format(l, p_val))\n",
    "    else:\n",
    "        print('Null hypothesis is rejected at lag = {} for p-val = {}'.format(l, p_val))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'\\nThe above results show that ACF is essentially random in the differenced DJIA Close values\\n'"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"\"\"\n",
    "The above results show that ACF is essentially random in the differenced DJIA Close values\n",
    "\"\"\""
   ]
  }
 ],
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